Thursday, December 3, 2009

Meter-as-rhythm (after Hasty)

Where London's theory respects a traditional distinction between rhythm and meter, Christopher Hasty actively seeks to break that distinction down by arguing that meter must be continually reinvented in listening: for example, he asserts that "meter, even when viewed from the perspective of metrical type, is fully particular and never 'the same'" (131). (London, on the other hand, cites cognition studies to argue that meter is internalized and therefore becomes a set of expectations that are maintained until strongly contradicted.)

Hasty's theory is based on projection: an attack and a duration project the possibility of another attack and duration, the simplest of which would be a repetition of the first (the solid arrow in (a) of the graphic shows a realized projection, the dotted slur that follows the potential of the same kind, the longer arrow marked Q a longer potential projection).

The simplest pattern in a 3/4 meter is shown in (b). As Hasty observes, triple meter is decidedly more complex than duple meter because
The third beat cannot function exactly like the second beat simply to continue the duration begun "before" there were any beats, for now that there is a second beat there is also a real potential for projecting a half-note duration (the potential Q in [the] example). In order to function as a continuation, the beginning of the third beat must deny this potential. In contrast, the beginning of the second beat denied no potential--rather, it created one projection and the potential for another. (132)
Given the consistency of temporal figuration in D779n13, a complete analysis on Hasty's terms would quickly become tedious, but his method may allow us a more nuanced view of the establishment of the hemiola pattern that is shown so plainly in Schachter's durational reduction. The familiar accompaniment pattern of bass and two afterbeats works out in a direct way through the first four beats the projection of triple meter we would expect from (b). In the next graphic, see P for quarter beats, R for the bar measure (the example is simplified as it shows only completed projections, not projective potential).

The repetition of R through bar 2 is sullied by some uncertainty as the entrance of the right hand figure creates an unusual two-beat anacrusis that sets up the possibility of an independent projection (Q). The completed projection of the left-hand figure through bar 2 eventually secures a two-bar hypermetric level (S), but the duple projections continue. Thus, the metric properties of the first three bars are all different: a simple development of 3/4 meter through quarter-note and bar-level projections (P, R); complicating the meter through a "superimposed" duple projection (Q); and establishment of a two-bar hypermeter (S) that includes both duple and triple projections.

Justin London. Hearing in Time: Psychological Aspects of Musical Meter. New York: Oxford University Press, 2004.
Christopher Hasty. Meter as Rhythm. New York and Oxford: Oxford University Press, 1997.